2,926 research outputs found
The Definition and Measurement of the Topological Entropy per Unit Volume in Parabolic PDE's
We define the topological entropy per unit volume in parabolic PDE's such as
the complex Ginzburg-Landau equation, and show that it exists, and is bounded
by the upper Hausdorff dimension times the maximal expansion rate. We then give
a constructive implementation of a bound on the inertial range of such
equations. Using this bound, we are able to propose a finite sampling algorithm
which allows (in principle) to measure this entropy from experimental data.Comment: 26 pages, 1 small figur
Abundance Analysis of the Halo Giant HD122563 with Three-Dimensional Model Stellar Atmospheres
We present a preliminary local thermodynamic equilibrium (LTE) abundance
analysis of the template halo red giant HD122563 based on a realistic,
three-dimensional (3D), time-dependent, hydrodynamical model atmosphere of the
very metal-poor star. We compare the results of the 3D analysis with the
abundances derived by means of a standard LTE analysis based on a classical,
1D, hydrostatic model atmosphere of the star. Due to the different upper
photospheric temperature stratifications predicted by 1D and 3D models, we find
large, negative, 3D-1D LTE abundance differences for low-excitation OH and Fe I
lines. We also find trends with lower excitation potential in the derived Fe
LTE abundances from Fe I lines, in both the 1D and 3D analyses. Such trends may
be attributed to the neglected departures from LTE in the spectral line
formation calculations.Comment: 4 pages, 4 figures, contribution to proceedings for Joint Discussion
10 at the IAU General Assembly, Rio de Janeiro, Brazil, August 200
A concentration inequality for interval maps with an indifferent fixed point
For a map of the unit interval with an indifferent fixed point, we prove an
upper bound for the variance of all observables of variables
which are componentwise Lipschitz. The proof is based on
coupling and decay of correlation properties of the map. We then give various
applications of this inequality to the almost-sure central limit theorem, the
kernel density estimation, the empirical measure and the periodogram.Comment: 26 pages, submitte
Three-dimensional models of metal-poor stars
I present here the main results of recent realistic, 3D, hydrodynamical
simulations of convection at the surface of metal-poor red giant stars. I
discuss the application of these convection simulations as time-dependent, 3D,
hydrodynamical model atmospheres to spectral line formation calculations and
abundance analyses. The impact of 3D models on derived elemental abundances is
investigated by means of a differential comparison of the line strengths
predicted in 3D under the assumption of local thermodynamic equilibrium (LTE)
with the results of analogous line formation calculations performed with
classical, 1D, hydrostatic model atmospheres. The low surface temperatures
encountered in the upper photospheric layers of 3D model atmospheres of very
metal-poor stars cause spectral lines of neutral metals and molecules to appear
stronger in 3D than in 1D calculations. Hence, 3D elemental abundances derived
from such lines are significantly lower than estimated by analyses with 1D
models. In particular, differential 3D1D LTE abundances for C, N, and O
derived from CH, NH, and OH lines are found to be in the range -0.5 to -1 dex.
Large negative differential 3D-1D corrections to the Fe abundance are also
computed for weak low-excitation neutral Fe lines. The application of
metal-poor 3D models to the spectroscopic analysis of extremely iron-poor halo
stars is discussed.Comment: 14 pages, 8 figures, to appear in the proceedings of the conference
'A Stellar Journey' -- 23-27/June/2008, Uppsala, Swede
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